Question

What is the inverse of f(x)= 3x-9

Answer 1

If
`f^(-1)(x)` is the inverse of
`f(x)`, then

`f\left(f^(-1)(x)\right) = x`

Given

`f(x) = 3x-9`

composing with the inverse function gives

`f\left(f^(-1)(x)\right) = 3f^(-1)(x) - 9 = x`

Solve for the inverse:

`3f^(-1)(x)-9 = x \\\\ 3f^(-1)(x) = x+9 \\\\ \boxed{f^(-1)(x) = \frac x3 + 3}`